Robust Rauch-Tung-Striebel smoothing framework for heavy-tailed and/or skew noises

A novel robust Rauch-Tung-Striebel smoothing framework is proposed based on a generalized Gaussian scale mixture (GGScM) distribution for a linear state-space model with heavy-tailed and/or skew noises. The state trajectory, mixing parameters and unknown distribution parameters are jointly inferred using the variational Bayesian approach. As such, a major contribution of this work is unifying results within the GGScM distribution framework. Simulation and experimental results demonstrate that the proposed smoother has better accuracy than existing smoothers

NLOS mitigation in indoor localization by marginalized Monte Carlo Gaussian smoothing

One of the main challenges in indoor time-of-arrival (TOA)-based wireless localization systems is to mitigate non-line-of-sight (NLOS) propagation conditions, which degrade the overall positioning performance. The positive skewed non-Gaussian nature of TOA observations under LOS/NLOS conditions can be modeled as a heavy-tailed skew t-distributed measurement noise. The main goal of this article is to provide a robust Bayesian inference framework to deal with target localization under NLOS conditions. A key point is to take advantage of the conditionally Gaussian formulation of the skew t-distribution, thus being able to use computationally light Gaussian filtering and smoothing methods as the core of the new approach. The unknown non-Gaussian noise latent variables are marginalized using Monte Carlo sampling. Numerical results are provided to show the performance improvement of the proposed approach

Estimation Algorithms for Non-Gaussian State-Space Models with Application to Positioning

State-space models (SSMs) are used to model systems with hidden time-varying state and observable measurement output. In statistical SSMs, the state dynamics is assumed known up to a random term referred to as the process noise, and the measurements contain random measurement noise. Kalman filter (KF) and Rauch– Tung–Striebel smoother (RTSS) are widely-applied closed-form algorithms that provide the parameters of the exact Bayesian filtering and smoothing distributions for discrete-time linear statistical SSMs where the process and measurement noises follow Gaussian distributions. However, when the SSM involves nonlinear functions and/or non-Gaussian noises, the Bayesian filtering and smoothing distributions cannot in general be solved using closed-form algorithms. This thesis addresses approximate Bayesian time-series inference for two positioning-related problems where the assumption of Gaussian noises cannot capture all useful knowledge of the considered system’s statistical properties: map-assisted indoor positioning and positioning using time-delay measurements.The motion constraints imposed by the indoor map are typically incorporated in the position estimate using the particle filter (PF) algorithm. The PF is a Monte Carlo algorithm especially suited for statistical SSMs where the Bayesian posterior distributions are too complicated to be adequately approximated using a well-known distribution family with a low-dimensional parameter space. In mapassisted indoor positioning, the trajectories that cross walls or floor levels get a low probability in the model. In this thesis, improvements to three different PF algorithms for map-assisted indoor positioning are proposed and compared. In the wall-collision PF, weighted random samples, also known as particles, are moved based on inertial sensor measurements, and the particles that collide with the walls are downweighted. When the inertial sensor measurements are very noisy, map information is used to guide the particles such that fewer particles collide with the walls, which implies that more particles contribute to the estimation. When no inertial sensor information is used, the particles are moved along the links of a graph that is dense enough to approximate the set of expected user paths.Time-delay based ranging measurements of e.g. ultra-wideband (UWB) and Global Navigation Satellite Systems (GNSSs) contain occasional positive measurement errors that are large relative to the majority of the errors due to multipath effects and denied line of sight. In this thesis, computationally efficient approximate Bayesian filters and smoothers are proposed for statistical SSMs where the measurement noise follows a skew t -distribution, and the algorithms are applied to positioning using time-delay based ranging measurements. The skew t -distribution is an extension of the Gaussian distribution, which has two additional parameters that affect the heavytailedness and skewness of the distribution. When the measurement noise model is heavy-tailed, the optimal Bayesian algorithm is robust to occasional large measurement errors, and when the model is positively (or negatively) skewed, the algorithms account for the fact that most large errors are known to be positive (or negative). Therefore, the skew t -distribution is more flexible than the Gaussian distribution and captures more statistical features of the error distributions of UWB and GNSS measurements. Furthermore, the skew t -distribution admits a conditionally Gaussian hierarchical form that enables approximating the filtering and smoothing posteriors with Gaussian distributions using variational Bayes (VB) algorithms. The proposed algorithms can thus be computationally efficient compared to Monte Carlo algorithms especially when the state is high-dimensional. It is shown in this thesis that the skew-t filter improves the accuracy of UWB based indoor positioning and GNSS based outdoor positioning in urban areas compared to the extended KF. The skew-t filter’s computational burden is higher than that of the extended KF but of the same magnitude.Tila-avaruusmalleilla mallinnetaan järjestelmiä, joilla on tuntema-ton ajassa muuttuva tila sekä mitatattava ulostulo. Tilastollisissa tila-avaruusmalleissa järjestelmän tilan muutos tunnetaan lukuunotta-matta prosessikohinaksi kutsuttua satunnaista termiä, ja mittauk-set sisältävät satunnaista mittauskohinaa. Kalmanin suodatin sekäRauchin Tungin ja Striebelin siloitin ovat yleisesti käytettyjä sulje-tun muodon estimointialgoritmeja, jotka tuottavat tarkat bayesiläi-set suodatus- ja siloitusjakaumat diskreettiaikaisille lineaarisille ti-lastollisille tila-avaruusmalleille, joissa prosessi- ja mittauskohinatnoudattavat gaussisia jakaumia. Jos käsiteltyyn tila-avaruusmalliinkuitenkin liittyy epälineaarisia funktioita tai epägaussisia kohinoita,bayesiläisiä suodatus- ja siloitusjakaumia ei yleensä voida ratkais-ta suljetun muodon algoritmeilla. Tässä väitöskirjassa tutkitaan ap-proksimatiivista bayesiläistä aikasarjapäättelyä ja sen soveltamistakahteen paikannusongelmaan, joissa gaussinen jakauma ei mallinnariittävän hyvin kaikkea hyödyllistä tietoa tutkitun järjestelmän tilas-tollisista ominaisuuksista: kartta-avusteinen sisätilapaikannus sekäsignaalin kulkuaikamittauksiin perustuva paikannus.Sisätilakartan tuottamat liikerajoitteet voidaan liittää paikkaestimaat-tiin käyttäen partikkelisuodattimeksi kutsuttua algoritmia. Partik-kelisuodatin on Monte Carlo -algoritmi, joka soveltuu erityisesti ti-lastollisille tila-avaruusmalleille, joissa bayesiläisen posteriorijakau-man tiheysfunktio on niin monimutkainen, että sen approksimointitunnetuilla matalan parametridimension jakaumilla ei ole mielekäs-tä. Kartta-avusteisessa sisätilapaikannuksessa reitit, jotka leikkaavatseiniä tai kerrostasoja, saavat muita pienemmät todennäköisyydet.Tässä väitöskirjassa esitetään parannuksia kolmeen eri partikkelisuo-datusalgoritmiin, joita sovelletaan kartta-avusteiseen sisätilapaikan-vnukseen. Seinätörmayssuodattimessa painolliset satunnaisnäytteeteli partikkelit liikkuvat inertiasensorimittausten mukaisesti, ja sei-nään törmäävät partikkelit saavat pienet painot. Kun inertiasensori-mittauksissa on paljon kohinaa, partikkeleita voidaan ohjata siten,että seinätörmäysten määrä vähenee, jolloin suurempi osa partikke-leista vaikuttaa estimaattiin. Kun inertiasensorimittauksia ei käytetälainkaan, sisätilakartta voidaan esittää graafina, jonka kaarilla partik-kelit liikkuvat ja joka on riittävän tiheä approksimoimaan odotetta-vissa olevien reittien joukkoa.Esimerkiksi laajan taajuuskaistan radioista (UWB, ultra-wideband)tai paikannussatelliiteista saatavat radiosignaalin kulkuaikaan pe-rustuvat etäisyysmittaukset taas voivat sisältää monipolkuheijastus-ten ja suoran reitin estymisen aiheuttamia positiivismerkkisiä vir-heitä, jotka ovat huomattavan suuria useimpiin mittausvirheisiinverrattuna. Tässä väitöskirjassa esitetään laskennallisesti tehokkaitabayesiläisen suodattimen ja siloittimen approksimaatioita tilastol-lisille tila-avaruusmalleille, joissa mittauskohina noudattaa vinoat -jakaumaa. Vino t -jakauma on gaussisen jakauman laajennos, jasillä on kaksi lisäparametria, jotka vaikuttavat jakauman paksuhän-täisyyteen ja vinouteen. Kun mittauskohinaa mallintava jakaumaoletetaan paksuhäntäiseksi, optimaalinen bayesiläinen algoritmi eiole herkkä yksittäisille suurille mittausvirheille, ja kun jakauma olete-taan positiivisesti (tai negatiivisesti) vinoksi, algoritmit hyödyntävättietoa, että suurin osa suurista virheistä on positiivisia (tai negatiivi-sia). Vino t -jakauma on siis gaussista jakaumaa joustavampi, ja sillävoidaan mallintaa kulkuaikaan perustuvien mittausten virhejakau-maa tarkemmin kuin gaussisella jakaumalla. Vinolla t -jakaumalla onmyös ehdollisesti gaussinen esitys, joka soveltuu suodatus- ja siloi-tusposteriorien approksimointiin variaatio-Bayes-algoritmilla. Näinollen esitetyt algoritmit voivat olla laskennallisesti tehokkaampiakuin Monte Carlo -algoritmit erityisesti tilan ollessa korkeaulotteinen.Tässä väitöskirjassa näytetään, että vino-t -virhejakauman käyttö pa-rantaa UWB-radioon perustuvan sisätilapaikannuksen tarkkuuttasekä satelliittipohjaisen ulkopaikannuksen tarkkuutta kaupunkiym-päristössä verrattuna laajennettuun Kalmanin suodattimeen. Vino-t -suodatuksen laskennallinen vaativuus on suurempi mutta samaakertaluokkaa kuin laajennetun Kalmanin suodattimen

Estimation Algorithms for Non-Gaussian State-Space Models with Application to Positioning

State-space models (SSMs) are used to model systems with hidden time-varying state and observable measurement output. In statistical SSMs, the state dynamics is assumed known up to a random term referred to as the process noise, and the measurements contain random measurement noise. Kalman filter (KF) and Rauch– Tung–Striebel smoother (RTSS) are widely-applied closed-form algorithms that provide the parameters of the exact Bayesian filtering and smoothing distributions for discrete-time linear statistical SSMs where the process and measurement noises follow Gaussian distributions. However, when the SSM involves nonlinear functions and/or non-Gaussian noises, the Bayesian filtering and smoothing distributions cannot in general be solved using closed-form algorithms. This thesis addresses approximate Bayesian time-series inference for two positioning-related problems where the assumption of Gaussian noises cannot capture all useful knowledge of the considered system’s statistical properties: map-assisted indoor positioning and positioning using time-delay measurements.The motion constraints imposed by the indoor map are typically incorporated in the position estimate using the particle filter (PF) algorithm. The PF is a Monte Carlo algorithm especially suited for statistical SSMs where the Bayesian posterior distributions are too complicated to be adequately approximated using a well-known distribution family with a low-dimensional parameter space. In mapassisted indoor positioning, the trajectories that cross walls or floor levels get a low probability in the model. In this thesis, improvements to three different PF algorithms for map-assisted indoor positioning are proposed and compared. In the wall-collision PF, weighted random samples, also known as particles, are moved based on inertial sensor measurements, and the particles that collide with the walls are downweighted. When the inertial sensor measurements are very noisy, map information is used to guide the particles such that fewer particles collide with the walls, which implies that more particles contribute to the estimation. When no inertial sensor information is used, the particles are moved along the links of a graph that is dense enough to approximate the set of expected user paths.Time-delay based ranging measurements of e.g. ultra-wideband (UWB) and Global Navigation Satellite Systems (GNSSs) contain occasional positive measurement errors that are large relative to the majority of the errors due to multipath effects and denied line of sight. In this thesis, computationally efficient approximate Bayesian filters and smoothers are proposed for statistical SSMs where the measurement noise follows a skew t -distribution, and the algorithms are applied to positioning using time-delay based ranging measurements. The skew t -distribution is an extension of the Gaussian distribution, which has two additional parameters that affect the heavytailedness and skewness of the distribution. When the measurement noise model is heavy-tailed, the optimal Bayesian algorithm is robust to occasional large measurement errors, and when the model is positively (or negatively) skewed, the algorithms account for the fact that most large errors are known to be positive (or negative). Therefore, the skew t -distribution is more flexible than the Gaussian distribution and captures more statistical features of the error distributions of UWB and GNSS measurements. Furthermore, the skew t -distribution admits a conditionally Gaussian hierarchical form that enables approximating the filtering and smoothing posteriors with Gaussian distributions using variational Bayes (VB) algorithms. The proposed algorithms can thus be computationally efficient compared to Monte Carlo algorithms especially when the state is high-dimensional. It is shown in this thesis that the skew-t filter improves the accuracy of UWB based indoor positioning and GNSS based outdoor positioning in urban areas compared to the extended KF. The skew-t filter’s computational burden is higher than that of the extended KF but of the same magnitude.Tila-avaruusmalleilla mallinnetaan järjestelmiä, joilla on tuntema-ton ajassa muuttuva tila sekä mitatattava ulostulo. Tilastollisissa tila-avaruusmalleissa järjestelmän tilan muutos tunnetaan lukuunotta-matta prosessikohinaksi kutsuttua satunnaista termiä, ja mittauk-set sisältävät satunnaista mittauskohinaa. Kalmanin suodatin sekäRauchin Tungin ja Striebelin siloitin ovat yleisesti käytettyjä sulje-tun muodon estimointialgoritmeja, jotka tuottavat tarkat bayesiläi-set suodatus- ja siloitusjakaumat diskreettiaikaisille lineaarisille ti-lastollisille tila-avaruusmalleille, joissa prosessi- ja mittauskohinatnoudattavat gaussisia jakaumia. Jos käsiteltyyn tila-avaruusmalliinkuitenkin liittyy epälineaarisia funktioita tai epägaussisia kohinoita,bayesiläisiä suodatus- ja siloitusjakaumia ei yleensä voida ratkais-ta suljetun muodon algoritmeilla. Tässä väitöskirjassa tutkitaan ap-proksimatiivista bayesiläistä aikasarjapäättelyä ja sen soveltamistakahteen paikannusongelmaan, joissa gaussinen jakauma ei mallinnariittävän hyvin kaikkea hyödyllistä tietoa tutkitun järjestelmän tilas-tollisista ominaisuuksista: kartta-avusteinen sisätilapaikannus sekäsignaalin kulkuaikamittauksiin perustuva paikannus.Sisätilakartan tuottamat liikerajoitteet voidaan liittää paikkaestimaat-tiin käyttäen partikkelisuodattimeksi kutsuttua algoritmia. Partik-kelisuodatin on Monte Carlo -algoritmi, joka soveltuu erityisesti ti-lastollisille tila-avaruusmalleille, joissa bayesiläisen posteriorijakau-man tiheysfunktio on niin monimutkainen, että sen approksimointitunnetuilla matalan parametridimension jakaumilla ei ole mielekäs-tä. Kartta-avusteisessa sisätilapaikannuksessa reitit, jotka leikkaavatseiniä tai kerrostasoja, saavat muita pienemmät todennäköisyydet.Tässä väitöskirjassa esitetään parannuksia kolmeen eri partikkelisuo-datusalgoritmiin, joita sovelletaan kartta-avusteiseen sisätilapaikan-vnukseen. Seinätörmayssuodattimessa painolliset satunnaisnäytteeteli partikkelit liikkuvat inertiasensorimittausten mukaisesti, ja sei-nään törmäävät partikkelit saavat pienet painot. Kun inertiasensori-mittauksissa on paljon kohinaa, partikkeleita voidaan ohjata siten,että seinätörmäysten määrä vähenee, jolloin suurempi osa partikke-leista vaikuttaa estimaattiin. Kun inertiasensorimittauksia ei käytetälainkaan, sisätilakartta voidaan esittää graafina, jonka kaarilla partik-kelit liikkuvat ja joka on riittävän tiheä approksimoimaan odotetta-vissa olevien reittien joukkoa.Esimerkiksi laajan taajuuskaistan radioista (UWB, ultra-wideband)tai paikannussatelliiteista saatavat radiosignaalin kulkuaikaan pe-rustuvat etäisyysmittaukset taas voivat sisältää monipolkuheijastus-ten ja suoran reitin estymisen aiheuttamia positiivismerkkisiä vir-heitä, jotka ovat huomattavan suuria useimpiin mittausvirheisiinverrattuna. Tässä väitöskirjassa esitetään laskennallisesti tehokkaitabayesiläisen suodattimen ja siloittimen approksimaatioita tilastol-lisille tila-avaruusmalleille, joissa mittauskohina noudattaa vinoat -jakaumaa. Vino t -jakauma on gaussisen jakauman laajennos, jasillä on kaksi lisäparametria, jotka vaikuttavat jakauman paksuhän-täisyyteen ja vinouteen. Kun mittauskohinaa mallintava jakaumaoletetaan paksuhäntäiseksi, optimaalinen bayesiläinen algoritmi eiole herkkä yksittäisille suurille mittausvirheille, ja kun jakauma olete-taan positiivisesti (tai negatiivisesti) vinoksi, algoritmit hyödyntävättietoa, että suurin osa suurista virheistä on positiivisia (tai negatiivi-sia). Vino t -jakauma on siis gaussista jakaumaa joustavampi, ja sillävoidaan mallintaa kulkuaikaan perustuvien mittausten virhejakau-maa tarkemmin kuin gaussisella jakaumalla. Vinolla t -jakaumalla onmyös ehdollisesti gaussinen esitys, joka soveltuu suodatus- ja siloi-tusposteriorien approksimointiin variaatio-Bayes-algoritmilla. Näinollen esitetyt algoritmit voivat olla laskennallisesti tehokkaampiakuin Monte Carlo -algoritmit erityisesti tilan ollessa korkeaulotteinen.Tässä väitöskirjassa näytetään, että vino-t -virhejakauman käyttö pa-rantaa UWB-radioon perustuvan sisätilapaikannuksen tarkkuuttasekä satelliittipohjaisen ulkopaikannuksen tarkkuutta kaupunkiym-päristössä verrattuna laajennettuun Kalmanin suodattimeen. Vino-t -suodatuksen laskennallinen vaativuus on suurempi mutta samaakertaluokkaa kuin laajennetun Kalmanin suodattimen

Robust human motion tracking using wireless and inertial sensors

Recently, miniature inertial measurement units (IMUs) have been deployed as wearable devices to monitor human motion in an ambulatory fashion. This thesis presents a robust human motion tracking algorithm using the IMU and radio-based wireless sensors, such as the Bluetooth Low Energy (BLE) and ultra-wideband (UWB). First, a novel indoor localization method using the BLE and IMU is proposed. The BLE trilateration residue is deployed to adaptively weight the estimates from these sensor modalities. Second, a robust sensor fusion algorithm is developed to accurately track the location and capture the lower body motion by integrating the estimates from the UWB system and IMUs, but also taking advantage of the estimated height and velocity obtained from an aiding lower body biomechanical model. The experimental results show that the proposed algorithms can maintain high accuracy for tracking the location of a sensor/subject in the presence of the BLE/UWB outliers and signal outages

Nonlinear Gaussian Filtering : Theory, Algorithms, and Applications

By restricting to Gaussian distributions, the optimal Bayesian filtering problem can be transformed into an algebraically simple form, which allows for computationally efficient algorithms. Three problem settings are discussed in this thesis: (1) filtering with Gaussians only, (2) Gaussian mixture filtering for strong nonlinearities, (3) Gaussian process filtering for purely data-driven scenarios. For each setting, efficient algorithms are derived and applied to real-world problems

Efficient Reinforcement Learning using Gaussian Processes

This book examines Gaussian processes (GPs) in model-based reinforcement learning (RL) and inference in nonlinear dynamic systems. First, we introduce PILCO, a fully Bayesian approach for efficient RL in continuous-valued state and action spaces when no expert knowledge is available. PILCO learns fast since it takes model uncertainties consistently into account during long-term planning and decision making. Thus, it reduces model bias, a common problem in model-based RL. Due to its generality and efficiency, PILCO is a conceptual and practical approach to jointly learning models and controllers fully automatically. Across all tasks, we report an unprecedented degree of automation and an unprecedented speed of learning. Second, we propose principled algorithms for robust filtering and smoothing in GP dynamic systems. Our methods are based on analytic moment matching and clearly advance state-of-the-art methods

Machine Learning Developments in Dependency Modelling and Feature Extraction

Three complementary feature extraction approaches are developed in this thesis which addresses the challenge of dimensionality reduction in the presence of multivariate heavy-tailed and asymmetric distributions. First, we demonstrate how to improve the robustness of the standard Probabilistic Principal Component Analysis by adapting the concept of robust mean and covariance estimation within the standard framework. We then introduce feature extraction methods that extend the standard Principal Component Analysis by exploring distribution-based robustification. This is achieved via Probabilistic Principal Component Analysis (PPCA), in which new, statistically robust variants are derived, also treating missing data. We propose a novel generalisation to the t-Student Probabilistic Principal Component methodology which (1) accounts for asymmetric distribution of the observation data, (2) is a framework for grouped and generalised multiple-degree-of-freedom structures, which provides a more flexible framework to model groups of marginal tail dependence in the observation data, and (3) separates the tail effect of the error terms and factors. The new feature extraction methods are derived in an incomplete data setting to efficiently handle the presence of missing values in the observation vector. We discuss statistical properties of their robustness. In the next part of this thesis, we demonstrate the applicability of feature extraction methods to the statistical analysis of multidimensional dynamics. We introduce the class of Hybrid Factor models that combines classical state-space model formulations with incorporation of exogenous factors. We show how to utilize the information obtained from features extracted using introduced robust PPCA in a modelling framework in a meaningful and parsimonious manner. In the first application study, we show the applicability of robust feature extraction methods in the real data environment of financial markets and combine the obtained results with a stochastic multi-factor panel regression-based state-space model in order to model the dynamic of yield curves, whilst incorporating regression factors. We embed the rank-reduced feature extractions into a stochastic representation of state-space models for yield curve dynamics and compare the results to classical multi-factor dynamic Nelson-Siegel state-space models. This leads to important new representations of yield curve models that can have practical importance for addressing questions of financial stress testing and monetary policy interventions which can efficiently incorporate financial big data. We illustrate our results on various financial and macroeconomic data sets from the Euro Zone and international markets. In the second study, we develop a multi-factor extension of the family of Lee-Carter stochastic mortality models. We build upon the time, period and cohort stochastic model structure to include exogenous observable demographic features that can be used as additional factors to improve model fit and forecasting accuracy. We develop a framework in which (a) we employ projection-based techniques of dimensionality reduction that are amenable to different structures of demographic data; (b) we analyse demographic data sets from the patterns of missingness and the impact of such missingness on the feature extraction; (c) we introduce a class of multi-factor stochastic mortality models incorporating time, period, cohort and demographic features, which we develop within a Bayesian state-space estimation framework. Finally (d) we develop an efficient combined Markov chain and filtering framework for sampling the posterior and forecasting. We undertake a detailed case study on the Human Mortality Database demographic data from European countries and we use the extracted features to better explain the term structure of mortality in the UK over time for male and female populations. This is compared to a pure Lee-Carter stochastic mortality model, demonstrating that our feature extraction framework and consequent multi-factor mortality model improves both in-sample fit and, importantly, out-of-sample mortality forecasts by a non-trivial gain in performance

Urban Informatics

This open access book is the first to systematically introduce the principles of urban informatics and its application to every aspect of the city that involves its functioning, control, management, and future planning. It introduces new models and tools being developed to understand and implement these technologies that enable cities to function more efficiently – to become ‘smart’ and ‘sustainable’. The smart city has quickly emerged as computers have become ever smaller to the point where they can be embedded into the very fabric of the city, as well as being central to new ways in which the population can communicate and act. When cities are wired in this way, they have the potential to become sentient and responsive, generating massive streams of ‘big’ data in real time as well as providing immense opportunities for extracting new forms of urban data through crowdsourcing. This book offers a comprehensive review of the methods that form the core of urban informatics from various kinds of urban remote sensing to new approaches to machine learning and statistical modelling. It provides a detailed technical introduction to the wide array of tools information scientists need to develop the key urban analytics that are fundamental to learning about the smart city, and it outlines ways in which these tools can be used to inform design and policy so that cities can become more efficient with a greater concern for environment and equity

Urban Informatics

This open access book is the first to systematically introduce the principles of urban informatics and its application to every aspect of the city that involves its functioning, control, management, and future planning. It introduces new models and tools being developed to understand and implement these technologies that enable cities to function more efficiently – to become ‘smart’ and ‘sustainable’. The smart city has quickly emerged as computers have become ever smaller to the point where they can be embedded into the very fabric of the city, as well as being central to new ways in which the population can communicate and act. When cities are wired in this way, they have the potential to become sentient and responsive, generating massive streams of ‘big’ data in real time as well as providing immense opportunities for extracting new forms of urban data through crowdsourcing. This book offers a comprehensive review of the methods that form the core of urban informatics from various kinds of urban remote sensing to new approaches to machine learning and statistical modelling. It provides a detailed technical introduction to the wide array of tools information scientists need to develop the key urban analytics that are fundamental to learning about the smart city, and it outlines ways in which these tools can be used to inform design and policy so that cities can become more efficient with a greater concern for environment and equity